This invention is in the field of hand-manipulated puzzles, as well as the teaching of geometric principles. More specifically, the invention concerns a puzzle formed of a set of different polyhedrons which can be assembled together in different ways to form solid geometric shapes such as rectangular solids.
Numerous geometric puzzles have been known in the past, both in two dimensions, as in plane geometry, and in three dimensions, as in solid geometry. However, none has demonstrated spatial relationships, symmetry, dissection of polyhedral solids, congruent triangles and other geometric and physical relationships as well as the set of polyhedrons and puzzle apparatus of this invention.
In the polyhedron puzzle of the invention, a clear plastic container or housing is provided in one embodiment, in a selected geometric shape such as a rectangular solid or a cube. The plastic container is closed at five sides and open at one side to enable assembling of the polyhedron puzzle pieces into the interior of the container. In a specific embodiment, three or more different shapes of polyhedrons are provided as puzzle pieces, each being solid throughout.
In one preferred embodiment of the invention, different shapes of polyhedrons of the set of polyhedrons are in different colors--for example, the colors blue, green and yellow can be used, or blue, green, yellow and red. The set preferably includes a five-sided polyhedron, comprised of a regular tetrahedron and an irregular tetrahedron as formed together along a matching triangular plane of each tetrahedron. These five-sided polyhedrons can all be replaced, or some of them can be replaced, with separate regular tetrahedrons and irregular tetrahedrons which, when one of each is laid together in the puzzle, will form the five-sided polyhedron. Similarly, a regular octahedron which may be included in set of polyhedrons may be replaced by four irregular tetrahedrons. These substitutions create additional configurations for assembly of the polyhedrons into the clear container or housing, which may be in the form of a cube.
Another aspect of the invention is that all of the polyhedrons included in the set are of the same density. This can enable a teacher to demonstrate, for example, that the five-sided polyhedron is equivalent to the combination of the regular tetrahedron and the irregular tetrahedron, by using a balance scale. In a specific form of the invention, the density of all polyhedrons is the same as that of water, i.e. a specific gravity of 1.0. This property can be used to demonstrate, by displacement of water, that certain combinations of shapes are equal in volume to other polyhedral shapes. Since water is the standard substance used to measure and express weight/volume relationships (density), when any piece of specific gravity 1.0 is caused to displace its own weight in water, this allows both weight and volume comparisons to be made. To demonstrate such relationships, one can use a graduated beaker and a balance scale, or even a coffee can filled to capacity in a pie tin. One can insert various combinations of pieces of the puzzle and show various weight/volume relationships to each other (or to multiples of each other) and to the whole. Volume, surface area and displacement can be demonstrated, with this easily used manipulative device. Obviously, the invention provides ways to demonstrate and to physically verify (and reinforce) what can be calculated mathematically.
With a set of polyhedrons in accordance with the invention, students learn to visualize and think more clearly about spatial relationships, dissection of solid shapes, matching triangles, volume of geometric objects and other geometric and physical relationships. The puzzle, including the clear container in the shape of a cube, for example, helps teach students to consider shapes in the context of negative space, somewhat like putting together a puzzle but in three dimensions, and demonstrates concepts of surface area.
In addition, polyhedron puzzles according to the invention provide challenge and enjoyment along with the learning of relationships in solid geometry.
It is therefore among the objects of the invention to teach some of the principles of solid geometry, spatial relationships, symmetry and dissection of solid shapes, through the provision of a puzzle which is enjoyable to manipulate and to solve. These and other objects, advantages and features of the invention will be apparent from the following description of a preferred embodiment, considered along with the accompanying drawings.